The state of stress near the singularities created by a plane punch

An attempt is made to obtain photoelastically the stress distribution in the near vicinity of singular points, when a punch is indenting an elastic half-plane. The punch is to be assumed flat and rough so that friction is developed between the contact surfaces. By expanding the complex stress function into a Taylor series, an extrapolation law is obtained, which allows the calculation of stresses at the vicinity of the singular points by means of photoelastic measurements at positions remote from these points. The error limits of this technique are defined and, finally, a relation between the order of singularity and the parameters of the photoelastic pattern is established.